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Home , Multivariate statistics

RESEARCH ESSENTIALS SEMINAR Evaluating Your : Types of Data and Basic Tests of Association

L. H. Domenico, PhD, RN, CARN [email protected] Learning Objectives

1. Describe the different types of data commonly encountered within medical research 2. Critically examine the theoretical principles guiding selected and multivariate statistical approaches 3. Identify key factors that influence the selection of appropriate statistical approaches for addressing relevant research questions It’s about finding the right instrument to address the problem at hand! It’s about using established protocols Choosing the Right : The Decision Making Process

1. What type of data will your measures render? – Identify the nature of each of your variables 2. What questions do you want to address? – Is there a relationship between age and level of optimism? – Are older people more optimistic than younger people? 3. How many Independent (predictor) Variables and Dependent (outcome) Variables will you have? 4. Decide whether a parametric or non-parametric statistical technique is appropriate Today’s Topics

1. Identifying the nature of your variables – Levels of measurement – Descriptive 2. Determining the type of question you want to answer – Preliminary (univariate statistics) – Univariate statistics – Multivariate statistics ■ Statistical techniques for explore relationships among variables ■ Statistical techniques to compare groups 3. Deciding whether a parametric or non-parametric statistical technique is appropriate – What to do if your data are not normally distributed? 1. IDENTIFYING THE NATURE OF YOUR VARIABLES Comparison of Measurement Levels

• At each successive measurement Ratio level, there is more information, and greater analytic flexibility.

• If you start with ratio or interval Interval measures, you can collapse information to a lower-level measure, but the reverse is not Ordinal true.

• Higher-level scales are usually (though not always) preferred. Nominal Order of Statistical Analyses

• Univariate 1 •

• Bivariate 2 • Relationships/associations

• Multivariate 3+ • Relationships btw 3 or more variables Descriptive Statistics

■ Used to: – Describe the characteristics of your – Check for any violation of the assumptions underlying the statistical techniques that you will use to address your research questions – Address specific research questions ■ Categorical variables – Frequencies, Percent ■ Continuous variables – , , , Distribution ( & ) 2. DETERMINING THE TYPE OF QUESTION YOU WANT TO ANSWER Statistical Techniques to Explore Relationships Among Variables

■ Correlation ■ ■ Multiple regression ■ ■ ■ Chi-square Correlation (Pearson product ())

■ Purpose – To describe the strength and direction of the linear relationship between two variables ■ Sample research question – Is there a relationship between age and optimism scores? Does optimism increase with age? ■ Type of variables needed – Two continuous variables Partial Correlation

■ Purpose – Similar to Pearson product-moment correlation, except that it allows you to control for an additional variable ■ Sample research question – After controlling for the effects of socially desirable responding, is there still a significant relationship between optimism and life satisfaction scores? ■ Type of variables needed – Three continuous variables Multiple Regression

■ Purpose – A family of techniques used to explore the relationship between one continuous DV and a number of IVs or predictors ■ Sample research question – How much of the in life satisfaction scores can be explained by the following variables: self-esteem, optimism and perceived control? – Which of these variables is a better predictor of life satisfaction? ■ Type of variables needed – One continuous DV – Two or more continuous IVs Logistic Regression

■ Purpose – A family of techniques used to explore the relationship between one or more categorical DV and two or more categorical and/or continuous IVs or predictors ■ Sample research question – What factors predict the likelihood that respondents would report that they had a problem with their sleep? ■ Type of variables needed – Two or more continuous or categorical predictor IVs – One categorical (dichotomous) DV (e.g. problem with sleep: Yes/No) Factor Analysis

■ Purpose ■ Sample research question – What is the underlying structure of the items that make up the Positive and Negative Affect Scale? – How many factors are involved ■ Type of variables needed – Set of related continuous variables (e.g. items of the Positive and Negative Affect Scale Chi-square (test for independence)

■ Purpose – To explore the relationship between two categorical variables. Compares the observed frequencies or proportions of cases that occur in each of the categories with the values that would be expected if there was not association between the two variables being measured ■ Sample research question – What is the relationship between gender and dropout rates from therapy? ■ Type of variables needed – Two categorical variables, with two or more categories in each (e.g. Gender- Male/Female; Drop out- yes/no)One categorical Statistical Techniques to Compare Groups

■ T-tests ■ One-way (ANOVA) ■ Two-way between-groups ANOVA ■ Multivariate analysis of variance (MANOVA) ■ Analysis of (ANCOVA) ■ Chi-square T-Tests

Independent-samples t-test Paired-samples t-test

■ Purpose ■ Purpose – To compare the mean scores of two – To compare the mean scores for the same group of people on two different different groups of people or occasions, or when you have matched conditions pairs ■ Sample research question ■ Sample research question – Are males more optimistic than – Does ten weeks of meditation training females? result in a decrease in participants’ level of anxiety? ■ Type of variables needed – One categorical IV with only two ■ Type of variables needed groups (e.g. Sex: Males/Females) – One categorical IV (e.g. Time: Time 1; Time 2) – One continuous DV – One continuous DV measured on two different occasions or under different conditions One-Way Analysis of Variance (ANOVA)

■ Purpose – To determine if there are significant differences in the mean scores on the DV across three or more groups. ■ Sample research question – Is there a difference in optimism scores for people who are under 30, between 31-49 and 50 years and over? ■ Type of variables needed – One categorical IV with three or more groups (e.g. Age: under 30; between 31-49 and 50 plus) – One continuous DV Two-Way Between-Groups ANOVA

■ Purpose – To simultaneously test for the effect of each of your IVs on the DV and also identifies any effect ■ Sample research question – What is the effect of age and gender on optimism scores? – Does gender moderate the relationship between age and optimism? ■ Type of variables needed – Two categorical IVs (e.g. Sex: males/females; age group: under 30; 31-49; 50+) – One continuous DV Multivariate Analysis of Variance (MANOVA) ■ Purpose – To compare two or more groups in terms of their on a group of DVs. Tests the null hypothesis that the population means on a set of DVs do not vary across different levels of a factor or grouping variable. ■ Sample research question – Do males and females differ in terms of overall well-being? – Are males healthier than females in terms of their general physical and psychological health (operationalized as anxiety, depression levels and perceived stress)? ■ Type of variables needed – One categorical IV – Two or more continuous DVs that are related (e.g. negative affect, positive affect, perceived stress) (ANCOVA)

■ Purpose – Used when you have a two-group pre-test/post-test design. The scores on the pre-test are treated as a covariate to control for pre-existing differences between the groups. ■ Sample research question – Is there a significant difference in the Fear of Statistics Test scores for participants in the math skills group and the confidence-building group, while controlling for their pre-test scores on this test? ■ Type of variables needed – One categorical IV with two or more levels (e.g. group 1/group 2) – One continuous DV (e.g. Fear of Statistics Test scores at Time 2) – One or more continuous covariates (e.g. Fear of Statistics Test scores at Time 1) Chi-square ()

■ Purpose – The chi-squared test is used to determine whether there is a significant difference between the expected frequencies and the observed frequencies in one or more categories. ■ Sample research question – Are males more likely to drop out of therapy than females? ■ Type of variables needed – One categorical IV with two groups (e.g. Sex: Males/Females) – One continuous DV 3. DECIDING WHETHER A PARAMETRIC OR NON- PARAMETRIC STATISTICAL TECHNIQUE IS APPROPRIATE Parametric vs. Non-

■ Parametric comes from parameter, or characteristic of a population ■ Parametric tests make assumptions about the population from which the sample has been drawn – This often includes assumptions about the shape of the population distribution (e.g. normally distributed) ■ Non-parametric tests do not have such stringent requirements and do not make assumptions about the underlying population distribution

■ Advantages: ■ Disadvantages: – Ideal when you have data that are – Tend to be less sensitive than measured on nominal (categorical) and their more powerful parametric ordinal (ranked) scales cousins – Accommodate very small samples ■ May fail to detect differences between groups that actually – Data do not meet the stringent exist assumptions of parametric techniques Purpose Sample Question Non-Parametric Statistic Parametric Counterpart

Exploring Is there a relationship between age and Spearman’s Rank Order Pearson product-moment Relationships optimism scores? Correlation (rho) correlation coefficient (r) What is the relationship between Chi-square gender and dropout rates from therapy? Comparing Is there a significant difference in the Mann-Whitney U Test Independent samples t- Groups mean self-esteem scores for males and test females? Is there a change in participants’ Wilcoxon Signed Rank Test Paired samples t-test anxiety scores from Time 1 to Time 2? Is there a difference in optimism scores Kruskal-Wallis Test One-way between groups for people who are under 35 years, 36- ANOVA 49 years and 50+ years? Is there a change in participant’s Two-way repeated anxiety scores from Time 1, Time 2 and measures ANOVA Time 3? Are males more likely to drop out of Chi-square therapy than females? Fields, A. (2017). Discovering Statistics Using IBM SPSS Statistics (J. Seaman Ed. 5th ed.). Thousand Oaks, CA: Sage Publications Ltd.

References

Fields, A. (2017). Discovering Statistics Using IBM SPSS Statistics (J. Seaman Ed. 5th ed.). Thousand Oaks, CA: Sage Publications Ltd.

Pallant, J. (2015). SPSS Survival Manual: A step by step guide to data analysis using SPSS (6th ed.). New York, NY: McGraw-Hill.

Polit, D. F. (2010). Statistics and Data Analysis for Nursing Research 2nd Edition. Upper Saddle River, NJ: Pearson.